One of the most spectacular manifestations of the quantum-mechanical nature of
fission is the phenomenon of spontaneous fission: without any stimulus from an
external source, atomic nuclei in theirs ground state spontaneously break apart.
Spontaneous fission is made possible by the tunneling effects of
quantum mechanics, namely the ability of systems to escape a stable potential
energy well (with some probability) [1]}. In classes of quantum
mechanics, examples of tunneling often involve a single particle of mass \(m\)  in
a one-dimensional potential well (and for educational purposes, such potentials
have often analytical forms such as a square well); in atomic nuclei, the
situation is a bit more complex for two reasons. First, the potential well is
defined in the collective space spanned by the collective coordinates
\(\mathbf {q}\)  introduced above. It is thus multi-dimensional and certainly not
analytical. Most importantly, the “mass” of the system in that collective
space is not the atomic mass of the nucleus or the nuclear binding energy. It
is in fact better thought of as the response of the nucleus to a change in
collective variable and is not a scalar but a rank-2 tensor. The role of this
collective mass tensor in determining tunneling probabilities is very important
as we will see in the next section.
